Flexural vibration element and electronic component

ABSTRACT

A flexural vibration element according to a first aspect of the invention includes: a vibration element body composed of a plurality of vibrating arms provided in parallel, a connecting part connecting the vibrating arms, and one central supporting arms extending between the vibrating arms from the connecting pert in parallel with the vibrating arms at equal distance from the arms and a frame body disposed outside the vibration element body.

This is a divisional of application Ser. No. 13/416,863 filed Mar. 9,2012 which is a continuation of application Ser. No. 12/647,868 filedDec. 28, 2009. The disclosure of the prior application is herebyincorporated by reference herein in its entirety.

BACKGROUND

1. Technical Field

The present invention relates to a flexural vibration element whichvibrates in a flexural vibration mode, and various electronic componentsincluding the flexural vibration element, such as a vibrator, aresonator, an oscillator gyro, and various sensors.

2. Related Art

As a piezoelectric vibration element in a flexural vibration mode, sucha tuning fork type piezoelectric vibration element has been widely usedthat a pair of vibrating arms is extended in parallel from a base partand the vibrating arms vibrate closer to or away from each other in ahorizontal direction. Vibration energy loss generated when the vibratingarms perform flexural vibration causes degradation of performances of avibrator such as increase of a CI value and decrease of a Q value.Therefore, various ways for preventing or reducing the vibration energyloss has been contrived.

JP-A-2002-261575 as a first example and JP-A-2004-260718 as a secondexample disclose a tuning fork type quartz crystal vibration element inwhich cuts or cut-grooves having a predetermined depth are formed atboth side parts of a base part from which vibrating arms extend. In thequartz crystal vibration element, even in a case where the vibratingarms generate vibration including a vertical component, vibration leakfrom the base part is suppressed by the cuts or the cut-grooves so as toimprove a trapping effect of the vibration energy and prevent variationof CI values among vibration elements.

Not only such the mechanical loss but also vibration energy loss isgenerated by heat conduction due to temperature difference between acompressive part and an extending part, which receives tensile stress,of the vibrating arms which performs flexural vibration. Decrease of theQ value caused by the heat conduction is called a thermoelastic effect.In order to prevent or suppress the decrease of the Q value due to thethermalelastic effect, Japanese Patent Application No. 63-110151 as athird example proposes a tuning fork type vibrator, in which a groove ora hole is formed on a centerline of a vibrating arm (vibrating beam)having a rectangular section.

The third example describes that the Q value becomes minimum when arelaxation frequency fm is expressed as fm=1/(2πτ) (here, π denotescircle ratio, τ denotes relaxation time) in a vibrator in a flexuralvibration mode. This is based on a relational equation of distortion andstress which is known in a case of internal friction, which is generallycaused by temperature difference, of a solid substance. A relationshipbetween a Q value and a frequency is generally expressed as a curve F ofFIG. 10 (refer to, for example, C. Zener et al., “Internal Friction inSolids III. Experimental Demonstration of Thermoelastic InternalFriction”, Physical Review, Volume 53, pp. 100-101 (January 1938)).Referring to FIG. 10, the Q value becomes a minimum value Q0 at arelaxation frequency f0 (=1/(2πτ)).

Here, it is also known that the relaxation frequency f0 can be obtainedfrom the following formula.f0=πk/(2ρC _(p) a ²)  (1)Here, π denotes circle ratio, k denotes a thermal conductivity invibration direction of the vibration part (flexural vibration part), ρdenotes a mass density of the vibration part (flexural vibration part),C_(p) denotes a heat capacity of the vibration part (flexural vibrationpart), and a denotes a width of the vibration part (flexural vibrationpart).

Further, JP-A-53-23588 as a fourth example discloses a quartz crystalvibrator in which a tuning fork type oscillation element having twovibrating arms is formed to be integrated with a holding frame, whichsurrounds the oscillation element and has a rectangular shape, at aconnecting part formed on a base part of the oscillation element. Thequartz crystal vibrator having such the structure is sealed bysandwiching the holding frame by planar covers from a top and a bottom.Further, JP-A-56-94813 as a fifth example discloses a tuning fork typepiezoelectric vibrator in which a vibrator and a rectangular supportingframe are connected by an elastic member provided on a lateral surfaceof a base part of the vibrator so as to suppress leak of vibrationenergy of vibrating arms from the base part to an outside.

On the other hand, as a flexural vibrator other than that of a tuningfork type, JP-A-2006-345519 as a sixth example discloses a resonator inwhich two parallel vibrating arms are coupled to each other by aconnecting part and a central arm is extended between the vibrating armsfrom the connecting part. The resonator is composed of asingle-component vibration element made of quartz crystal. In theresonator, at least one groove is formed on at least one of a frontsurface and a rear surface of the vibrating arms so as to make anexcitation electric field even and regionally-strong, reducing energyconsumption and limiting a CI value. Further, the groove of thevibrating arms is extended to the connecting part, at which mechanicalstress is maximum, and an electric field is extracted at this region soas to increase a vibration coupling effect of the vibrating arms.

Vibration elements vibrating in the flexural vibration mode include avibration element of an electrostatic driving type using electrostaticforce and a vibration element of a magnetic driving type using magnetismas well as the vibration element of the piezoelectric driving typedescribed above. JP-A-5-312576 as a seventh example discloses an angularvelocity sensor as a vibration element of the electrostatic drivingtype. In the angular velocity sensor, a first vibrating body composed ofa square frame part is supported by a first supporting beam so as to beable to vibrate in X-axis direction, and a second vibrating body havinga square plain plate shape is supported by a second supporting beam soas to be able to vibrate in Y-axis direction, on a substrate made of asilicon material. The first supporting beam bends due to electrostaticforce which is generated between a fixed conductive part provided on anend part of the substrate and a movable conductive part provided on anend part of the first vibrating body. Thus the first vibrating bodyvibrates in the X-axis direction. JP-A-2001-183140 as an eighth examplediscloses another angular velocity sensor as another vibration elementof the electrostatic driving type. This angular velocity sensor iscomposed of a sensor body made of a silicon wafer and a glass substrateopposed to the sensor body. The sensor body has plummets provided to aninside of a vibration frame, which is supported in a fixed frame by adriving beam, by multiple beams. The sensor body and the plummetsvibrate due to electrostatic force generated between parallel plainplate electrodes provided on the sensor body and the glass substrate.

Further, JP-B-43-1194 as a ninth example discloses a vibrating bodystructure as a vibration element of the magnetic driving type. In thevibrating body structure, a vibrating body made of a constant modulusmaterial is fixed and supported on an external fixing pedestal at itssupporting part at one end thereof. A spring part branched from aconnecting part between the vibrating body and the pedestal is drivenand vibrated by magnet fixed to a free end of the spring part and by anelectromagnetic coil fixed to a base. JP-A-10-19577 as a tenth examplediscloses an angular velocity sensor as another vibration element of themagnetic driving type. In the angular velocity sensor, a thin filmmagnet is disposed on a thin film vibrating plate which is composed of asilicon substrate and is supported as a cantilever beam. The thin filmvibrating plate is vibrated in a thickness direction by an effect ofelectromagnetic force generated by applying alternating current to aconductor or an electromagnetic coil provided outside the thin filmvibrating plate.

The inventor studied a means for suppressing vibration energy loss ofvibrating arms in a piezoelectric vibration element having such astructure that one central supporting arm was extended from a connectingpart between the two vibrating arms as illustrated in the sixth example.Especially, as far as the inventor knows, almost only the third examplestudies an influence of the above-mentioned thermoelastic effect givento the piezoelectric vibration element in a flexural vibration mode,among related arts.

FIG. 11A shows a typical example of a piezoelectric vibration elementhaving a related art structure including one central supporting arm.This piezoelectric vibration element 1 includes two vibrating arms 3 and4 extending from a connecting part 2 in parallel. Between the vibratingarms 3 and 4, one central supporting arm 5 extends in parallel with thearms 3 and 4 at equal distance from the arms 3 and 4. A linear groove 6is formed on each of a front surface and a rear surface of the vibratingarm 3 and a linear groove 7 is formed on each of a front surface and arear surface of the vibrating arm 4. The piezoelectric vibration element1 is fixed and held on a mount part 8 of a package or the like, which isnot shown, at an end part 5 a, which is opposite to an end at theconnecting part, of the central supporting arm 5. When a predeterminedvoltage is applied to an excitation electrode, which is not shown, inthis state, the vibrating arms 3 and 4 perform flexural vibration in adirection closer to or away from each other as shown by arrows in thedrawing.

Because of this flexural vibration, mechanical-compressive/-tensiledistortion occurred at the central supporting arm 5 in a longitudinaldirection of the arm 5. The distortion was observed astemperature-increase and temperature-decrease occurring in the centralsupporting arm 5. As shown in FIG. 11B, when the vibrating arms 3 and 4bend in a direction away from each other, the whole of the connectingpart 2 bends toward the end part 5 a of the central supporting arm 5.Therefore, the central supporting arm 5 receives stress compressing thearm 5 toward the end part 5 a. In an opposite manner, when the vibratingarms 3 and 4 bend in a direction coming closer to each other, theconnecting part 2 bends toward an opposite side of the end part 5 a ofthe central supporting arm 5 as shown in FIG. 11C. Therefore, thecentral supporting arm 5 receives stress pulling the arm 5 toward theopposite side of the end part 5 a.

As a result, part of the flexural vibration of the vibrating arms 3 and4 goes off from the central supporting arm 5 to the mount part 8, thatis, mechanical vibration leak occurs, causing increase of a CI value anddecrease of a Q value. Thus performance of a vibrator may be degraded.Further, compressive/tensile stress acting on the central supporting arm5 generates temperature gradient inside the piezoelectric vibrationelement 1. As a result, vibration energy loss due to the thermoelasticloss may be generated.

SUMMARY

An advantage of the present invention is to provide such a flexuralvibration element in a flexural vibration mode that mechanical lossand/or thermoelastic loss of vibration energy of a plurality ofvibrating arms are/is suppressed and performance thereof is improved. Inthe flexural vibration element, one central supporting arm extends froma connecting part between the vibrating arms.

A flexural vibration element according to a first aspect of theinvention includes: a vibration element body composed of a plurality ofvibrating arms provided in parallel, a connecting part connecting thevibrating arms, and one central supporting arm extending between thevibrating arms from the connecting part in parallel with the vibratingarms at equal distance from the arms; and a frame body disposed outsidethe vibration element body. In the flexural vibration element, thevibration element body is supported by the frame body at an end part,which is opposite to the connecting part, of the central supporting arm.

The connecting part of the vibration element body bends and vibrates dueto the flexural vibration of the vibrating arms and therefore thecompressive stress or the tensile stress acts along the centralsupporting arm in a longitudinal direction, bending and deforming theconnecting portion of the frame body with the central supporting part.However, the flexural vibration hardly acts on other portions of theframe body. Therefore, when the flexural vibration element of the firstaspect is fixed and supported on a package or the like at a portionother than the connecting portion of the frame body with the centralsupporting arm, vibration leak of the vibrating arms toward the outsidecan be suppressed. Thus the performance of the flexural vibrationelement can be improved.

The flexural vibration element of the invention may be a piezoelectricvibration element of a piezoelectric driving type which is used in avibrator, a resonator, a gyro, a piezoelectric device such as varioussensors, and other electronic components. Further, the flexuralvibration element of the invention may be a flexural vibration elementof an electrostatic driving type and that of a magnetic driving type.

In the flexural vibration element of the aspect, the end part, oppositeto the connecting part, of the central supporting arm may be directlyconnected with one side part of the frame body so as to support thevibration element body. Though the side part receives the compressivestress or the tensile stress due to the flexural vibration of thevibrating arms so as to bend and deform, other side parts are hardlyinfluenced by the flexural vibration. Therefore, vibration leak of thevibrating arms toward the outside can be suppressed by fixing andsupporting the flexural vibration element on a package or the like atother side parts.

In the flexural vibration element of the aspect, the side part, which isconnected with the central supporting arm, of the frame body may have agroove formed on at least one of a front surface and a rear surfacethereof, and the groove may be positioned in an area that is along theside part and in which compressive stress and tensile stress alternatelyoccur at an inner side and an outer side in a width direction of theside part due to flexural vibration of the vibrating arms. In the sidepart, temperature-increase due to compression and temperature-decreasedue to extension alternately occur at the inner side and the outer sidein the width direction of the side part so as to generate temperaturedifference between the inner side and the outer side, but heat transferbetween the inner side and the outer side can be limited by the grooveprovided on the side part. Accordingly, decrease of a Q value due tothermoelastic loss is suppressed, being able to achieve higherperformance of the flexural vibration element.

In the flexural vibration element of the aspect, the groove may beformed between one end of the side part and a part of the same to whichthe central supporting arm is connected and between the other end of theside part and the part to which the central supporting arm is connected.Accordingly, the thermoelastic loss can be effectively decreased and theQ value can be improved without losing strength and rigidity of the sidepart.

In the flexural vibration element of the aspect, the groove of the sidepart may have a bottom. Therefore, a heat transfer path between theinner side and the outer side in the width direction of the side part isnarrowed at an intermediate part thereof, which is equivalent toelongating the heat transfer path. As a result, a relaxation time τduring which the temperature becomes an equilibrium condition betweenthe inner side and the outer side of the side part becomes long.Therefore, a relaxation vibration frequency (f=1/(2πτ)) at the minimum Qvalue is lower than that in a case where the side part does not have agroove. In a range that the relaxation vibration frequency is higherthan that in the case without any groove, the Q value is higher.

In the flexural vibration element of the aspect, the groove of the sidepart may be a through groove. Accordingly, the heat transfer pathbetween the inner side and the outer side in the width direction of theside part is cut at an intermediate part thereof so as to be shorterthan that in a related art structure. As a result, a relaxation time τduring which the temperature becomes an equilibrium condition betweenthe inner side and the outer side in the width direction of the sidepart becomes short. Therefore, a relaxation vibration frequency(f=1/(2πτ)) at the minimum Q value is higher than that in a case wherethe side part does not have a groove. In a range that the relaxationvibration frequency is lower than that in the case without any groove,the Q value is higher.

In the flexural vibration element of the aspect, the frame body may havea supporting part, at an interior side thereof, extending between a pairof side parts thereof, and the end part, opposite to the connectingpart, of the central supporting arm may be connected to the supportingpart so as to support the vibration element body. Though the supportingpart receives the compressive stress or the tensile stress due to theflexural vibration of the vibrating arms so as to bend and deform, sideparts of the frame body are hardly influenced by the flexural vibration.Therefore, vibration leak of the vibrating arms toward the outside canbe suppressed by fixing and supporting the flexural vibration element ona package or the like at the side parts.

In the flexural vibration element of the aspect, the supporting part ofthe frame body may have a groove formed on at least one of a frontsurface and a rear surface thereof, and the groove may be positioned inan area that is along the supporting part and in which compressivestress and tensile stress alternately occur at a vibration element bodyside of the supporting part and an opposite side to the vibrationelement body side due to flexural vibration of the vibrating arms. Inthe supporting part, temperature-increase due to compression andtemperature-decrease due to extension alternately occur at the vibrationelement body side and the opposite side in the width direction of thesupporting part so as to generate temperature difference between thevibration element body side and the opposite side, but heat transferbetween the vibration element body side and the opposite side can belimited by the groove provided on the supporting part. Accordingly,decrease of a Q value due to thermoelastic loss is suppressed, beingable to achieve higher performance of the flexural vibration element.

In the flexural vibration element of the aspect, the groove may beformed between one end of the supporting part and a part of the same towhich the central supporting arm is connected and between the other endof the supporting part and the part to which the central supporting armis connected. Accordingly, the thermoelastic loss can be effectivelydecreased and the Q value can be improved without losing strength andrigidity of the supporting part.

In the flexural vibration element of the aspect, the groove of thesupporting part may have a bottom. Therefore, a heat transfer pathbetween the vibration element body side and the opposite side of thevibration element body side of the supporting part is narrowed at theintermediate part thereof, which is equivalent to elongating the heattransfer path. As a result, a relaxation time τ during which thetemperature becomes an equilibrium condition between the vibrationelement body side and the opposite side of the supporting part becomeslong. Therefore, a relaxation vibration frequency (f=1/(2πτ)) at theminimum Q value is lower than that in a case where the supporting partdoes not have a groove. In a range that the relaxation vibrationfrequency is higher than that in the case without any groove, the Qvalue is higher.

In the flexural vibration element of the aspect, the groove of thesupporting part may be a through groove. Accordingly, the heat transferpath between the vibration element body side and the opposite side ofthe vibration element body side of the supporting part is cut at anintermediate part thereof so as to be shorter than that in a related artstructure. As a result, a relaxation time τ during which the temperaturebecomes an equilibrium condition between the vibration element body sideand the opposite side of the supporting part becomes short. Therefore, arelaxation vibration frequency (f=1/(2πτ)) at the minimum Q value ishigher than that in a case where the supporting part does not have agroove. In a range that the relaxation vibration frequency is lower thanthat in the case without any groove, the Q value is higher.

An electronic component according to a second aspect of the inventionincludes: the flexural vibration element of the first aspect; a base onwhich the flexural vibration element is disposed; and a lid bonded withthe base. In the electronic component, the flexural vibration element isfixed to the base at a side part that is different from a side part towhich the central supporting arm of the frame body is connected, and isair-tightly sealed in a space formed by the base and the lid. Thus anelectronic component such as a piezoelectric device having a higher Qvalue and exhibiting higher performance than a related art is provided.

An electronic component according to a third aspect of the inventionincludes: the flexural vibration element of the first aspect; a basebonded to a lower surface of the frame body of the flexural vibrationelement; and a lid bonded to an upper surface of the frame body. In theelectronic component, the flexural vibration element is air-tightlysealed in a space formed by the base and the lid. Thus an electroniccomponent such as a piezoelectric device having a higher Q value andexhibiting higher performance than a related art is provided.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be described with reference to the accompanyingdrawings, wherein like numbers reference like elements.

FIG. 1A is a plan view showing a piezoelectric vibration element of afirst embodiment of the invention. FIGS. 1B and 1C are schematic viewsshowing deformation of vibrating arms due to flexural vibration.

FIG. 2A is a plan view showing a piezoelectric vibration element of afirst modification of the first embodiment. FIG. 2B is apartially-enlarged plan view showing a side part of a frame body. FIG.2C is a sectional view taken along a II-II line of FIG. 2B.

FIG. 3A is a partially-enlarged plan view showing a side part of a framebody of a piezoelectric vibration element of a second modification ofthe first embodiment. FIG. 3B is a sectional view taken along a III-IIIline of the FIG. 3A.

FIG. 4 is a longitudinal sectional view showing a piezoelectric deviceprovided with the piezoelectric vibration element of the firstembodiment.

FIG. 5A is a plan view showing a piezoelectric vibration element of asecond embodiment of the invention. FIGS. 5B and 5C are schematic viewsshowing deformation of vibrating arms due to flexural vibration.

FIG. 6A is a plan view showing a piezoelectric vibration element of afirst modification of the second embodiment. FIG. 6B is apartially-enlarged plan view showing a supporting part of a frame body.FIGS. 6C and 6D are sectional views respectively taken along a VIc-VIcline of FIG. 6B and along a VId-VId line of FIG. 6B.

FIG. 7A is a partially-enlarged plan view showing a supporting part of aframe body of a piezoelectric vibration element of a second modificationof the second embodiment. FIGS. 7B and 7C are sectional viewsrespectively taken along a VIIb-VIIb line of FIG. 7A and along aVIIc-VIIc line of FIG. 7A.

FIG. 8 is a longitudinal sectional view showing a piezoelectric deviceprovided with the piezoelectric vibration element of the secondembodiment.

FIG. 9 is a longitudinal sectional view showing another piezoelectricdevice provided with the piezoelectric vibration element of the secondembodiment.

FIG. 10 is a graph showing a relationship between relaxation frequencyand a minimum value of a Q value in a piezoelectric vibration element ofa flexural vibration mode.

FIG. 11A is a plan view showing a piezoelectric vibration element of arelated art. FIGS. 11B and 11C are schematic views showing deformationof vibrating arms due to flexural vibration.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Preferred embodiments of the invention will now be described withreference to the accompanying drawings. Here, elements common in thedrawings have the same reference numerals.

First Embodiment

FIG. 1A is a schematic view showing a structure of a piezoelectricvibration element, according to a first embodiment, to which the presentinvention is applied. A piezoelectric vibration element 11 according tothe first embodiment includes a vibration element body composed of aconnecting part 12, two vibrating arms 13 and 14 which extend from theconnecting part 12 in parallel, and one central supporting arm 15. Thecentral supporting arm 15 extends from the connecting part 12 betweenthe vibrating arms 13 and 14 in parallel with the arms 13 and 14 atequal distance from the arms 13 and 14. A linearly shaped long groove 16is formed on each of a front surface and a rear surface of the vibratingarm 13 and a linearly shaped long groove 17 is formed on each of a frontsurface and a rear surface of the vibrating arm 14, so as to control acrystal impedance (CI) value.

The piezoelectric vibration element 11 further includes a frame body 18having a rectangular shape and disposed at the outside of the vibrationelement body. The central supporting arm 15 is integrally connected withone side part 19 of the frame body 18 at an end part 15 a thereof whichis positioned opposite to the connecting part 12. Thus, the vibrationelement body is supported by the frame body 18 like a cantilever. Theframe body 18 may be formed to have round corners or chamfered edges.

The piezoelectric vibration element 11 is composed of a so-called Z-cutquartz crystal thin plate in which Y-axis of a quartz crystal axis isoriented in a longitudinal direction of the vibrating arms, X-axis isoriented in a width direction of the same, and Z-axis is oriented in anorthogonal direction of the front surface and the rear surface of thevibration element, like a related art tuning-fork type quartz crystalvibration element. The piezoelectric vibration element 11 may be made ofa piezoelectric material other than quartz crystal.

Though it is not shown, an excitation electrode is formed on surfaces,including inner surfaces of the grooves 16 and 17, of the vibrating arms13 and 14. When predetermined voltage is applied to the excitationelectrode in a state that the vibration element body is supported by theframe body 18 at the central supporting arm 15 thereof as a cantileveras described above, the vibrating arms 13 and 14 bend and vibrate closerto and away from each other in a horizontal direction as shown by arrowsin the drawing.

Because of the flexural vibration of the vibrating arms 13 and 14, theside part 19 of the frame body 18 bends and deforms in the horizontaldirection. As shown in FIG. 1B, when the vibrating arms 13 and 14 bendin a direction away from each other, the whole of the connecting part 12bends toward the end part 15 a of the central supporting arm 15.Accordingly, the central supporting arm 15 receives stress compressingthe arm 15 toward the end part 15 a side, bending the side part 19toward the outside of the frame body 18. Here, compressive stress actsalong an inner side, in a width direction, of the side part 19,especially, acts on parts 20 and 21 close to a part 15′ at which thecentral supporting arm 15 is connected with the frame body 18. Tensilestress acts along an outer side, in the width direction, of the sidepart 19, especially acts on a part 22 which has relatively a large areafrom the part 15′ as a center toward the both ends of the side part.

In an opposite manner, as shown in FIG. 1C, when the vibrating arms 13and 14 bend in a direction in which the arms come closer to each other,the whole of the connecting part 12 bends in an opposite direction to adirection toward the end part 15 a of the central supporting arm 15. Thecentral supporting arm 15 receives stress pulling the arm 15 from theend part 15 a side, bending the side part 19 toward the inside of theframe body 18. Therefore, tensile stress acts along the inner side, in awidth direction, of the side part 19, especially, acts on the parts 20and 21 close to the part 15′ at which the central supporting arm 15 isconnected with the frame body 18. Compressive stress acts along theouter side, in the width direction, of the side part 19, that is, actson the part 22, which has relatively a large area, from the part 15′ asa center toward the both ends of the side part.

In contrast, compressive stress and tensile stress hardly occur at aconnecting portion between the side part 19 and an adjacent side part ofthe frame body 18 and the surrounding part of the connecting portion.Accordingly, when the frame body 18 is fixed to a package or the like ata side part except for the side part 19 in the piezoelectric vibrationelement 11, vibration leak of the vibrating arms can be prevented orsuppressed. Thus performance of the piezoelectric vibration element 11can be improved.

First Modification of First Embodiment

FIGS. 2A to 2C show a first modification of the first embodiment. Apiezoelectric vibration element 11 of the first modification differsfrom the piezoelectric vibration element 11 of the first embodiment at apoint that the element of the first modification has grooves 23 and 24along the side part 19 of the frame body 18. The groove 23 is disposedbetween the part 20 at the inner side, in the width direction, of theside part 19 and the part 22 at the outer side of the same, at the samedistance from peripheries of the side part 19, and the groove 24 isdisposed between the part 21 at the inner side and the part 22, at thesame distance from peripheries of the side part 19. As described in thefirst embodiment, compressive stress and tensile stress occuralternately in the side part 19 due to the flexural vibration of thevibrating arms 13 and 14.

FIG. 2C shows a case where the vibrating arms bend away from each other,and accordingly the part 20 (21) at the inner side in the widthdirection of the side part 19 becomes a compressive side and the part 22at the outer side becomes a tensile side. As shown in FIG. 2C, thegrooves 23 and 24 have bottoms at the same depths from each of the frontand rear surfaces of the side part. In the drawing, + denotestemperature-increase, and − denotes temperature-decrease. Across thegroove 23 (24), a temperature increases at the part 20 (21) at thecompressive side and a temperature decreases at the part 22 at thetensile side. Because of this temperature gradient, heat transfers fromthe part 20 (21) at the compressive side (+) through a part at thegroove 23 (24) to the part 22 at the tensile side (−).

In an opposite manner, when the vibrating arms bend closer to eachother, the parts 20 and 21 at the inner side in the width direction ofthe side part 19 become a tensile side, and the part 22 at the outerside becomes a compressive side. The temperature increases at the part22 at the compressive side, and the temperature decreases at the parts20 and 21 at the tensile side. Because of this temperature gradient,heat transfers from the part 22 at the compressive side respectivelythrough parts at the grooves 23 and 24 to the parts 20 and 21 at thetensile side. Thus, the temperature gradient is generated between thepart 20 at the inner side in the width direction of the side part 19 andthe part 22 at the outer side and between the part 21 at the inner sideand the part 22 depending on a direction in which the vibrating armsbend closer to or away from each other, and the heat transfer occursdepending on the temperature gradient.

A heat transfer path between the part 20 and the part 22 and a heattransfer path between the part 21 and the part 22 are narrowed atintermediate parts thereof by the grooves 23 and 24 respectively. As aresult, a relaxation time τ1 during which the temperature becomes anequilibrium condition between the part 20 and the part 22 and betweenthe part 21 and the part 22 is longer than a relaxation time τ0 of thecase of the first embodiment in which the side part 19 does not have agroove. It can be considered that this is equivalent to a case where thewidth T of the side part 19 is increased to a width T1 as shown by animaginary line 19′ in FIG. 2C. Accordingly, the piezoelectric vibrationelement 11 of the present modification has a relaxation vibrationfrequency f10 which is expressed as f10 is lower than the relaxationvibration frequency f0 which is expressed as f0=1/(2πτ0) of the firstembodiment.

In view of a relationship between a frequency and a Q value in FIG. 10,a shape of a curve F is not changed, so that it can be considered thatthe curve F is shifted to a position of a curve F1, which is in afrequency lowering direction, with the lowering of the relaxationvibration frequency. Accordingly, in a range that a desired usingfrequency is higher than the vibration frequency f0, the Q value isalways higher than the minimum value Q0 of the first embodiment. Asabove, by providing the grooves 23 and 24 having the bottoms on the sidepart 19, mechanical loss of vibration energy and thermoelastic loss canbe suppressed and the Q value is further improved. Thus, highperformance of the piezoelectric vibration element 11 can be achieved.Further, a similar advantageous effect can be obtained in a case wherethe grooves having bottoms are provided only one of the front surfaceand the rear surface of the side part 19.

Second Modification of First Embodiment

FIGS. 3A and 3B show a second modification of the first embodiment. Adifferent point of the second modification from the first modificationis that the side part 19 of the second modification is provided with agroove 25 which penetrates through front and rear surfaces of the sidepart 19 (hereinafter, also referred to as a through groove 25) insteadof the groove having a bottom. The part 20 (21) at the inner side in thewidth direction of the side part 19 is separated from the part 22 at theouter side by the through groove 25.

As is the case of FIGS. 2A to 2C, when the vibrating arms bend andvibrate in a direction closer to or away from each other in thehorizontal direction, the side part 19 bends and deforms in thehorizontal direction. Inside the side part, compressive stress andtensile stress occur depending on a direction of the bend of the sidepart. A temperature increases at a compressive part, on which thecompressive stress acts, of the side part 19, and a temperaturedecreases at a tensile part on which the tensile stress acts.

FIG. 3B shows a case where the vibrating arms bend away from each other,and accordingly the inner side in the width direction of the side part19 is compressed and the outer side is extended. In the drawing, adegree of temperature-increase is expressed by the number of symbols: +,and a degree of temperature-decrease is expressed by the number ofsymbols:−. Regarding the whole of the side part 19, the temperatureincreases at the part 20 (21) at the compressive side and a temperaturedecreases at the part 22 at the tensile side. Since the through groove25 is formed in the second modification, heat transfer does not occurbetween the part 20 (21) at the inner side in the width direction of theside part 19 and the part 22 at the outer side.

In a local view, in a first part at a vibration element body side acrossthe groove 25 in the width direction of the side part 19, a magnitude ofcompressive stress acting on an inner side in the width direction of thefirst part is different from that acting on a groove 25 side of thefirst part. In the first part, the temperature-increase is larger at theinner side, that is, at the vibration element body side at which thecompressive stress is larger, and the temperature-increase is small atthe groove 25 side at which the compressive stress is smaller.Accordingly, in the inside of the first part, temperature gradient fromthe inner side (++) to the groove 25 side (+) is generated due to therelative difference between the temperature-increases, and heat transferoccurs along the temperature gradient.

In a similar manner, in a second part opposed to the first part, whichis positioned at the vibration element body side, across the groove 25in the width direction of the side part 19 as well, a magnitude oftensile stress acting on an outer side in the width direction of thesecond part is different from that acting on the groove 25 side of thesecond part. In the second part, the temperature-decrease is larger atthe outer side at which the tensile stress is larger, that is, at theopposite side to the vibration element body side, and thetemperature-decrease is smaller at the groove 25 side at which thetensile stress is smaller. Accordingly, in the inside of the secondpart, temperature gradient from the groove 25 side (−) to the outer side(−−) is generated due to the relative difference between thetemperature-decreases, and heat transfer occurs along the temperaturegradient.

In an opposite manner, in a case where the vibrating arms bend closer toeach other, the inner side in the width direction of the side part 19 isextended and the outer side is compressed. Accordingly, regarding thewhole of the side part 19, the temperature increases at the part 22 atthe compressive side and the temperature decreases at the part 20 (21)at the tensile side. When parts at both sides in the width direction ofthe side part 19 across the groove 25 are locally viewed, temperaturegradient from the outer side toward the groove 25 occurs in one part andtemperature gradient from the groove 25 side to the inner side occurs inthe other part, and heat transfer occurs along the respectivetemperature gradients.

In the second modification, a heat transfer path at each of the parts atthe both sides in the width direction of the side part 19 issubstantially shorter than that of the first embodiment due to thethrough groove 25. As a result, a relaxation time τ2 during which thetemperature becomes an equilibrium condition on each of the parts isshorter than the relaxation time τ0 of the first embodiment which doesnot have a through groove. It can be considered that this is equivalentto a case where the width T of the side part 19 is decreased to a widthT2 of each of the parts which are separated by the through groove 25.Accordingly, the piezoelectric vibration element of the secondmodification has a relaxation vibration frequency f20 which is expressedas f20=1/(2πτ2). Since τ2<τ0 is satisfied, the relaxation vibrationfrequency f20 is higher than the relaxation vibration frequency f0 whichis expressed as f0=1/(2πτ0) of the first embodiment.

In view of the relationship between a frequency and a Q value in FIG.10, the shape of the curve F is not changed, so that it can beconsidered that the curve F is shifted to a position of a curve F2,which is in a frequency rising direction, with the rise of therelaxation vibration frequency. Accordingly, in a range that a desiredusing frequency is lower than the vibration frequency f0, the Q value isalways higher than the minimum value Q0 of the first embodiment. Asabove, by providing the through groove 25 on the side part 19,mechanical loss of vibration energy and thermoelastic loss can besuppressed and the Q value is further improved. Thus, high performanceof the piezoelectric vibration element of the second modification can beachieved as is the case with the first modification shown in FIGS. 2A to2C.

FIG. 4 shows a piezoelectric device provided with the piezoelectricvibration element 11 of the first embodiment or the first or secondmodification of the second embodiment. This piezoelectric device 31includes a base 32 having a rectangular box shape and formed by layeringthin plates made of an insulating material, and a lid 33 having a planarshape. The piezoelectric vibration element 11 is mounted in a space 34of the base 32 in a manner to be fixed to mounts 35 and 36 at its bothside parts adjacent to the side part 19 of the frame body 18 with aconductive adhesive or the like. By bonding the lid 33 on an upper endof the base 32, the piezoelectric vibration element 11 is air-tightlysealed inside the piezoelectric device 31. Here, the base 32 and the lid33 may have different shapes. For example, the base 32 may have a planarshape and the lid 33 may have a box shape, or the base 32 and the lid 33both may have a box shape, so as to form a space for mounting thepiezoelectric vibration element 11 therein.

Second Embodiment

FIG. 5A is a schematic view showing a structure of a piezoelectricvibration element, according to a second embodiment, to which thepresent invention is applied. In a similar manner to the firstembodiment, a piezoelectric vibration element 41 according to the secondembodiment includes a vibration element body composed of a connectingpart 42, two vibrating arms 43 and 44 which extend from the connectingpart 42 in parallel, and one central supporting arm 45. The centralsupporting arm 45 extends from the connecting part 42 between thevibrating arms 13 and 14 in parallel with the arms 13 and 14 at equaldistance from the arms 13 and 14. A linearly shaped long groove 46 isformed on each of a front surface and a rear surface of the vibratingarm 43 and a linearly shaped long groove 47 is formed on each of a frontsurface and a rear surface of the vibrating arm 44, so as to control acrystal impedance (CI) value.

The piezoelectric vibration element 41 further includes a frame body 48having a rectangular shape and disposed at the outside of the vibrationelement body. The frame body 48 of the second embodiment has asupporting part 49 which is a bar extending between a pair of side partswhich are positioned respectively at right and left sides of the drawingto be opposed to each other. The supporting part 49 is disposed to beadjacent to one side part (upper side in the drawing) of the frame body48 in parallel with the one side part. The central supporting arm 45 isintegrally connected with the supporting part 49 at an end part 45 athereof which is positioned opposite to the connecting part 42. Thus,the vibration element body is supported by the frame body 48 like acantilever.

The piezoelectric vibration element 41 of the second embodiment is alsocomposed of a so-called Z-cut quartz crystal thin plate which is setsuch that Y-axis of a quartz crystal axis is oriented in a longitudinaldirection of the vibrating arms, X-axis is oriented in a width directionof the arms, and Z-axis is oriented in an orthogonal direction of thefront surface and the rear surface of the vibration element, like arelated art tuning-fork type quartz crystal vibration element. Thepiezoelectric vibration element 41 may be made of a piezoelectricmaterial other than quartz crystal.

Though it is not shown, an excitation electrode is formed on surfaces,including inner surfaces of the grooves 46 and 47, of the vibrating arms43 and 44. When a predetermined voltage is applied to the excitationelectrode in a state that the vibration element body is supported by theframe body 48 at the central supporting arm 45 thereof as a cantileveras described above, the vibrating arms 43 and 44 bend and vibrate closerto and away from each other in a horizontal direction as shown by arrowsin the drawing.

Because of the flexural vibration of the vibrating arms 13 and 14, thesupporting part 49 of the frame body 48 bends and deforms in thehorizontal direction. As shown in FIG. 5B, when the vibrating arms 43and 44 bend in a direction away from each other, the whole of theconnecting part 42 bends toward the end part 45 a of the centralsupporting arm 45. Accordingly, the central supporting arm 45 receivesstress compressing the arm 45 toward the end part 45 a, bending thesupporting part 49 toward the side part, adjacent to the part 49, of theframe body 48. Therefore, compressive stress acts along an inner side,in a width direction, of the supporting part 49, especially, acts onparts 50 and 51 close to a part 45′ at which the central supporting arm45 is connected with the supporting part 49. Tensile stress acts alongan outer side, in the width direction, of the supporting part 49 fromthe part 45′ as a center toward the both ends of the supporting part 49,that is, acts on a part 52 which roughly corresponds to the parts 50 and51. Further, around connecting portions of the supporting part 49 withthe frame body 48, tensile stress acts on parts 53 and 54 at an innerside in the width direction of the supporting part 49 and compressivestress acts on parts 55 and 56 at an outer side of the part 49.

In an opposite manner, as shown in FIG. 5C, when the vibrating arms 43and 44 bend in a direction in which the arms come closer to each other,the whole of the connecting part 42 bends in a direction opposite to theend part 45 a of the central supporting arm 45. The central supportingarm 45 receives stress pulling the arm 45 from the end part 45 a,bending the supporting part 49 toward the vibration element body.Therefore, tensile stress acts along the inner side in the widthdirection of the supporting part 49, especially, acts on the parts 50and 51 close to the part 45′ at which the central supporting arm 45 isconnected with the supporting part 49. Compressive stress acts along anouter side, in the width direction, of the supporting part 49 from thepart 45′ as a center toward the both ends of the supporting part 49,that is, acts on the part 52 which roughly corresponds to the parts 50and 51. Further, around the connecting portions of the supporting part49 with the frame body 48, compressive stress acts on the parts 53 and54 at the inner side in the width direction of the supporting part 49and tensile stress acts on the parts 55 and 56 at the outer side of thepart 49.

In contrast, compressive stress and tensile stress due to the vibratingarms 43 and 44 hardly occur in each of the side parts of the frame body48. Accordingly, when the piezoelectric vibration element 41 issupported in a package or the like by fixing the side parts of the framebody 48 thereof to the package or the like, vibration leak of thevibrating arms can be prevented or suppressed. Thus performance of thepiezoelectric vibration element 41 can be improved.

First Modification of Second Embodiment

FIGS. 6A to 6D show a first modification of the second embodiment. Apiezoelectric vibration element 41 of the first modification differsfrom the piezoelectric vibration element 41 of the second embodiment ata point that the element of the first modification has grooves 57, 58,59, and 60 along the supporting part 49. The grooves 57, 58, 59, and 60are respectively disposed between the part 50 at the inner side, in thewidth direction, of the supporting part 49 and the part 52 at the outerside of the same, between the part 51 at the inner side and the part 52,between the part 53 at the inner side and the part 55, and between thepart 54 at the inner side and the part 56 at the outer side, at equaldistance from peripheries of the supporting part 49. As describedaccording to the second embodiment above, compressive stress and tensilestress occur alternately at the supporting part 49 due to the flexuralvibration of the vibrating arms 43 and 44.

FIG. 6C shows a case where the part 50 (51) at the inner side in thewidth direction of the supporting part 49 becomes a compressive side andthe part 52 at the outer side becomes a tensile side when the vibratingarms bend away from each other. FIG. 6D shows a case where the part 55(56) at the outer side in the width direction of the supporting part 49becomes a compressive side and the part 53 (54) at the inner sidebecomes a tensile side when the vibrating arms bend away from eachother. As shown in FIGS. 6C and 6D, the grooves 57 to 60 have bottoms atthe same depths from each of front and rear surfaces of the supportingpart 49. In the drawing, + denotes temperature-increase, and − denotestemperature-decrease. Across the groove 57 (58), a temperature increasesat the part 50 (51) at the compressive side and a temperature decreasesat the part 52 at the tensile side. In a similar manner, across thegroove 59 (60), a temperature increases at the part 55 (56) at thecompressive side and a temperature decreases at the part 53 (54) at thetensile side. Because of these temperature gradients, heat transferoccurs from the part 50 (51) at the compressive side through a part atthe groove 57 (58) to the part 52 at the tensile side (−) and from thepart 55 (56) at the compressive side through a part at the groove 59(60) to the part 53 (54) at the tensile side respectively.

In an opposite manner, when the vibrating arms bend closer to eachother, the parts 50 and 51 at the inner side in the width direction ofthe supporting part 49 and the parts 55 and 56 at the outer side becomea tensile side, and the part 52 at the outer side and the parts 53 and54 at the inner side become a compressive side. The temperatureincreases at the parts 52, 53, and 54 at the compressive side, and thetemperature decreases at the parts 50, 51, 55, and 56 at the tensileside. Because of these temperature gradients, heat transfers from thepart 52 at the compressive side through parts at the grooves 57 and 58respectively to the parts 50 and 51 at the tensile part, and from theparts 53 and 54 at the compressive side respectively through parts atthe grooves 59 and 60 to the parts 55 and 56 at the tensile side. Thusthe heat transfers in a direction opposite to the direction of the abovecase. Thus, the temperature gradient is generated between the part 50 atthe inner side in the width direction of the supporting part 49 and thepart 52 at the outer side, between the part 51 at the inner side and thepart 52, between the part 53 at the inner side and the part 55 at theouter side, and between the part 54 at the inner side and the part 56 atthe outer side respectively, depending on a direction in which thevibrating arms bend closer to or away from each other, and the heattransfer occurs depending on the temperature gradient.

Heat transfer paths between the part 50 and the part 52, between thepart 51 and the part 52, between the part 53 and the part 55, andbetween the part 54 and the part 56 are narrowed at intermediate partsthereof respectively by the grooves 57, 58, 59, and 60. As a result, arelaxation time τ1 during which the temperature becomes an equilibriumcondition between the part 50 and the part 52, between the part 51 andthe part 22, between the part 55 and the part 53, and between the part56 and the part 54 is longer than a relaxation time τ0 of the case ofthe second embodiment in which the supporting part 49 does not have agroove. It can be considered that this is equivalent to a case where thewidth T of the supporting part 49 is increased to a width T1 as shown byimaginary lines 49′ and 49″ respectively in FIGS. 6C and 6D.Accordingly, the piezoelectric vibration element 41 of the presentmodification has a relaxation vibration frequency f10 which is expressedas f10=1(2πτ=1). Since τ1>τ0 is satisfied, the relaxation vibrationfrequency f10 is lower than the relaxation vibration frequency f0 whichis expressed as f0=1/(2πτ0) of the second embodiment.

In view of the relationship between a frequency and a Q value in FIG.10, the shape of the curve F is not changed, so that it can beconsidered that the curve F is shifted to the position of the curve F1,which is in a frequency lowering direction, with the lowering of therelaxation vibration frequency. Accordingly, in a range that a desiredusing frequency is higher than the vibration frequency f0, the Q valueis always higher than the minimum value Q0 of the second embodiment. Byproviding the grooves 57 to 60 having the bottoms on the supporting part49 of the piezoelectric vibration element 41 as above, mechanical lossof vibration energy and thermoelastic loss can be suppressed and the Qvalue is further improved. Thus, high performance of the piezoelectricvibration element 41 can be achieved. Here, the same advantageous effectcan be offered also in a case where the grooves having bottoms areformed one of the front surface and the rear surface of the supportingpart 49.

Second Modification of Second Embodiment

FIGS. 7A and 7B show a second modification of the second embodiment. Adifferent point of the second modification from the first modificationshown in FIGS. 6A to 6D is that the supporting part 49 of the secondmodification has grooves 61 and 62 which penetrate from a front surfacethrough to a rear surface of the supporting part 49 (hereinafter, alsoreferred to as through grooves 61 and 62) instead of the grooves havingbottoms. The part 50 (51) at the inner side in the width direction ofthe supporting part 49 is separated from the part 52 at the outer sideby the through groove 61 and the part 53 (54) at the inner side isseparated from the part 55 (56) at the outer side by the through groove62.

As is the case of FIGS. 6A to 6D, when the vibrating arms bend andvibrate in a direction closer to or away from each other in thehorizontal direction, the supporting part 49 bends and deforms in thehorizontal direction. Inside the supporting part 49, compressive stressand tensile stress occur depending on a direction of the bend of thesupporting part 49. A temperature increases at a compressive part, onwhich the compressive stress acts, of the supporting part 49, and atemperature decreases at a tensile part on which the tensile stressacts.

FIG. 7B shows a case where the part 50 (51) at the inner side in thewidth direction of the supporting part 49 becomes a compressive side andthe part 52 at the outer side becomes a tensile side around a connectingpart 45′ at which the central supporting arm 45 is connected with thesupporting part 49, when the vibrating arms bend away from each other.FIG. 7C shows a case where the part 55 (56) at the outer side in thewidth direction of the supporting part 49 becomes a compressive side andthe part 53 (54) at the inner side becomes a tensile side, aroundconnecting parts of the supporting part 49 with the side part of theframe body 48. In the drawing, a degree of temperature-increase isexpressed by the number of symbols: +, and a degree oftemperature-decrease is expressed by the number of symbols: −. Regardingthe whole of the supporting part 49, the temperature increases at thepart 50 (51) and the part 55 (56) at the compressive sides and atemperature decreases at the part 52 and the part 53 (54) at the tensilesides. Since the through grooves 61 and 62 are formed in the secondmodification, heat transfer does not occur between the part 50 (51) atthe inner side and the part 52 at the outer side and between the part 53(54) at the inner side and the part 55 (56) at the outer side.

In a local view, in a first part at a vibration element body side of thesupporting part 49 across the groove 61 in the width direction of thesupporting part 49, a magnitude of compressive stress acting on an innerside (vibration element body side) in the width direction of the firstpart is different from that acting on a groove 61 side of the firstpart. In the first part, the temperature-increase is larger at the innerside, that is, at the vibration element body side at which thecompressive stress is larger, and the temperature-increase is smaller atthe groove 61 side at which the compressive stress is smaller, as shownin FIG. 7B. Accordingly, in the inside of the first part, temperaturegradient from the inner side (++) to the groove 61 side (+) is generateddue to the relative difference between the temperature-increases, andheat transfer occurs along the temperature gradient.

In a similar manner, in a second part opposed to the first part acrossthe groove 61 in the width direction of the supporting part 49 as well,a magnitude of tensile stress acting on an outer side in the widthdirection of the second part is different from that acting on the groove61 side of the second part. In the second part, the temperature-decreaseis larger at the outer side at which the tensile stress is larger, thatis, at the opposite side to the vibration element body side, and thetemperature-decrease is smaller at the groove 61 side at which thetensile stress is smaller. Accordingly, in the inside of the secondpart, temperature gradient from the groove 61 side (−) to the outer side(−−) is generated due to the relative difference between thetemperature-decreases, and heat transfer occurs along the temperaturegradient.

In a similar manner, in a third part opposed to a part, which ispositioned at the vibration element body side, across the groove 62 inthe width direction of the supporting part 49, a magnitude ofcompressive stress acting on an outer side in the width direction of thethird part is different from that acting on a groove 62 side of thethird part. In the third part, the temperature-increase is larger at theouter side at which the compressive stress is larger, that is, at anopposite side to the vibration element body side, and thetemperature-increase is smaller at the groove 62 side at which thecompressive stress is smaller, as shown in FIG. 7C. Accordingly, in theinside of the third part, temperature gradient from the outer side (++)to the groove 62 side (+) is generated due to the relative differencebetween the temperature-increases, and heat transfer occurs along thetemperature gradient.

In a similar manner, in a fourth part at the vibration element body sideacross the groove 62 in the width direction of the supporting part 49 aswell, a magnitude of tensile stress acting on an outer side in the widthdirection of the fourth part is different from that acting on a groove62 side of the fourth part. In the fourth part, the temperature-decreaseis larger at the inner side at which the tensile stress is larger, thatis, at the vibration element body side, and the temperature-decrease issmaller at the groove 62 side at which the tensile stress is smaller.Accordingly, in the inside of the fourth part, temperature gradient fromthe groove 62 side (−) to the inner side (−−) is generated due to therelative difference between the temperature-decreases, and heat transferoccurs along the temperature gradient.

In an opposite manner, when the vibrating arms bend closer to eachother, the inner side in the width direction of the supporting part 49is extended and the outer side is compressed around the connecting part45′ at which the central supporting arm 45 is connected with thesupporting part 49. Around the connecting portions of the supportingpart 49 with the side part of the frame body 48, the inner side in thewidth direction is compressed and the outer side is extended.Accordingly, regarding the whole of the supporting part 49, thetemperature increases at the parts 52, 53, and 54 at the compressivesides and the temperature decreases at the parts 50, 51, 55, and 56 atthe tensile sides.

In a local view, in the second part, which is at the opposite side tothe vibration element body side, across the groove 61 in the widthdirection of the supporting part 49, the magnitude of compressive stressacting on the outer side in the width direction of the second part isdifferent from that acting on the groove 61 side of the second part. Inthe second part, the temperature-increase is larger at the outer side atwhich the compressive stress is larger, that is, at the opposite side tothe vibration element body side, and the temperature-increase is smallerat the groove 61 side at which the compressive stress is smaller. Thus,in the inside of the second part, temperature gradient from the outerside to the groove 61 side is generated due to the relative differencebetween the temperature-increases, and heat transfer occurs along thetemperature gradient.

In a similar manner, in the first part at the vibration element bodyside across the groove 61 in the width direction of the supporting part49 as well, the magnitude of tensile stress acting on the inner side inthe width direction of the first part is different from that acting onthe groove 61 side of the first part. In the first part, thetemperature-decrease is larger at the inner side at which the tensilestress is larger, that is, at the vibration element body side, and thetemperature-decrease is smaller at the groove 61 side at which thetensile stress is smaller. Thus, in the inside of the first part,temperature gradient from the groove 61 side to the inner side isgenerated due to the relative difference between thetemperature-decreases, and heat transfer occurs along the temperaturegradient.

In a similar manner, in the fourth part at the vibration element bodyside across the groove 62 in the width direction of the supporting part49, the magnitude of compressive stress acting on the inner side in thewidth direction of the fourth part is different from that acting on thegroove 62 side of the fourth part. In the fourth part, thetemperature-increase is larger at the inner side at which thecompressive stress is larger, that is, at the vibration element bodyside, and the temperature-increase is smaller at the groove 62 side atwhich the compressive stress is smaller. Thus, in the inside of thefourth part, temperature gradient from the inner side to the groove 62side is generated due to the relative difference between thetemperature-increases, and heat transfer occurs along the temperaturegradient.

In a similar manner, in the third part opposed to the fourth part acrossthe groove 62 in the width direction of the supporting part 49 as well,the magnitude of tensile stress acting on the outer side in the widthdirection of the third part is different from that acting on the groove62 side of the third part. In the third part, the temperature-decreaseis larger at the outer side at which the tensile stress is larger, thatis, at the opposite side to the vibration element body side, and thetemperature-decrease is smaller at the groove 62 side at which thetensile stress is smaller. Thus, in the inside of the third part,temperature gradient from the groove 62 side to the outer side isgenerated due to the relative difference between thetemperature-decreases, and heat transfer occurs along the temperaturegradient.

In the second modification, a heat transfer path inside each of thefirst to fourth parts at the inner side and the outer side in the widthdirection of the supporting part 49 is substantially shortened by thethrough grooves 61 and 62 compared to the second embodiment. As aresult, a relaxation time τ2 during which the temperature becomes anequilibrium condition on each of the parts is shorter than therelaxation time τ0 of the second embodiment which does not have athrough groove. It can be considered that this is equivalent to a casewhere the width T of the supporting part 49 is decreased to a width T2of each of the first part and the second part which are separated by thethrough groove 61 and the third part and the fourth part which areseparated by the through groove 62. Accordingly, the piezoelectricvibration element of the second modification has a relaxation vibrationfrequency f20 which is expressed as f20=1/(2πτ2). Since τ2<τ0 issatisfied, the relaxation vibration frequency f20 is higher than therelaxation vibration frequency f0, which is expressed as f0=1/(2πτ0), ofa related art structure.

In view of the relationship between a frequency and a Q value in FIG.10, the shape of the curve F is not changed, so that it can beconsidered that the curve F is shifted to a position of the curve F2,which is in a frequency rising direction, with the rise of therelaxation vibration frequency. Accordingly, in a range that a desiredusing frequency is lower than the vibration frequency f0, the Q value isalways higher than the minimum value Q0 of the second embodiment. Byproviding the through grooves 61 and 62 on the supporting part 49 asabove, mechanical loss of vibration energy and thermoelastic loss can besuppressed and the Q value is further improved. Thus, high performanceof the piezoelectric vibration element of the second modification can beachieved as is the case with the first modification shown in FIGS. 6A to6D.

FIG. 8 shows a piezoelectric device provided with the piezoelectricvibration element 41 of the second embodiment or the first or secondmodification of the second embodiment. This piezoelectric device 71includes a base 72 disposed under the piezoelectric vibration element 41and having a planar shape, and a lid 73 disposed above the piezoelectricvibration element 41 and having a planar shape. The piezoelectricvibration element 41 is air-tightly bonded to the base 72 and the lid 73respectively at a lower surface and an upper surface of the frame body48 with sealants 74 and 75 made of low-melting glass. Accordingly, thevibration element body is supported by the supporting part 49 as acantilever and is air-tightly sealed inside the piezoelectric device 71.Here, the shapes of the base 72 and the lid 73 are not limited to theplanar shape. For example, the peripheries, which are bonded with theframe body 48 of the piezoelectric vibration element 41, of the base andthe lid may be formed thick, or a groove, a concave part, or a convexpart may be formed on surfaces facing the piezoelectric vibrationelement or outer surfaces of the base and the lid.

FIG. 9 shows another piezoelectric device provided with thepiezoelectric vibration element 41 of the second embodiment or the firstor second modification of the second embodiment. This piezoelectricdevice 81 includes a base 82 having a rectangular box shape and formedby layering thin plates made of an insulating material, and a lid 83having a planar shape. The piezoelectric vibration element 41 is mountedinside a space 84 of the base 82 by fixing the frame body 48 on mounts85 and 86 with a conductive adhesive or the like. By bonding the lid 83on an upper end of the base 82, the piezoelectric vibration element 41is air-tightly sealed inside the piezoelectric device 81. Here, the base82 and the lid 83 may have different shapes. For example, the base 82may have a planar shape and the lid 83 may have a box shape, or the base82 and the lid 83 both may have a box shape, so as to form a space formounting the piezoelectric vibration element 41 therein.

The invention is not limited to the above embodiments but may beembodied by adding various kinds of modifications and alterationswithout departing from the technical scope of the invention. Forexample, the present invention is applicable to a piezoelectricvibration element in which three or more vibrating arms extend from aconnecting part. Further, a flexural vibration element of the aboveembodiments is formed in one body with the piezoelectric material, butmay be formed by providing a piezoelectric plate material on a surfaceof a silicon semiconductor or the like. Further, the present inventionis applicable not only to a flexural vibration element of apiezoelectric driving type but also to that of an electrostatic drivingtype or a magnetic driving type. In this case, the flexural vibrationelement may be made of a known material such as silicon semiconductor aswell as the piezoelectric material. Further, the flexural vibrationelement of the invention is applicable to various electronic componentsas well as the piezoelectric device.

The entire disclosure of Japanese Patent Application No. 2008-335550,filed Dec. 27, 2008 is expressly incorporated by reference herein.

What is claimed is:
 1. A flexural vibration element comprising: a vibration element body composed of a plurality of vibrating arms provided in parallel, a connecting part connecting the vibrating arms, and one central supporting arm extending between the vibrating arms from the connecting part in parallel with the vibrating arms at equal distance from the vibrating arms; and a frame body disposed outside the vibration element body, the frame body being a rectangular frame that completely surrounds the vibration element body in plan view, the vibration element body being supported by the frame body at an end part of the central supporting arm, the end part being opposite to the connecting part, the vibrating arms, the connecting part, the central supporting arm and the frame body being integrally formed as one piece from a single material with a fixed positional relationship between the central supporting arm and the frame body, wherein the frame body has a supporting part, at an interior side thereof, extending between a pair of side parts thereof, and the end part, opposite to the connecting part, of the central supporting arm is connected to the supporting part so as to support the vibration element body.
 2. The flexural vibration element according to claim 1, wherein the supporting part has a groove formed on at least one of a front surface and a rear surface thereof, and the groove is positioned in an area that is along the supporting part and in which compressive stress and tensile stress alternately occur at a vibration element body side of the supporting part and an opposite side to the vibration element body side due to flexural vibration of the vibrating arms.
 3. The flexural vibration element according to claim 2, wherein the groove is formed between one end of the supporting part and a part of the same to which the central supporting arm is connected and between the other end of the supporting part and the part to which the central supporting arm is connected.
 4. The flexural vibration element according to claim 2, wherein the groove has a bottom.
 5. The flexural vibration element according to claim 2, wherein the groove is a through groove.
 6. An electronic component, comprising: the flexural vibration element of claim 1; a base bonded to a lower surface of the frame body of the flexural vibration element; and a lid bonded to an upper surface of the frame body, wherein the flexural vibration element is air-tightly sealed in a space formed by the base and the lid.
 7. An electronic component; comprising: the flexural vibration element of claim 1; a base on which the flexural vibration element is disposed; and a lid bonded with the base; wherein the flexural vibration element is fixed on the base at a side part of the frame body, and the flexural vibration element is air-tightly sealed in a space formed by the base and the lid. 